Mean centering continuous covariates for a group fMRI analysis

Probably one of the most frequently asked questions on the FSL list is how/when you should mean center continuous covariates. The following chart breaks down different contrasts for common models using continuous covariates and explains whether or not mean centering the continuous covariate is necessary. If you have any questions or helpful suggestions for this web page, feel free to email me.

If you do mean center a covariate in a model be sure that the numbers entered into the design matrix are precise. If you de-mean in Excel or Matlab and then only enter 2 significant digits in your FSL design matrix file, the resulting covariate may be far from "mean centered" and throw off P-values and interpretations. If mean centering include at least four significant digits in your design matrix file to be safe.

Also important is that if you have multiple groups (see third model example) you should not mean center within each group separately. The reason for this is that your continuous covariate may actually describe some of the group differences, and then mean centering within group will remove this important aspect of the covariate. For example, if you have two groups and one is significantly younger than the other, this difference in ages between groups may explain brain activation differences. If you mean center age within each group, then each group's set of ages will be centered about the same value, 0, and then you risk detecting group differences that are actually just attributable to age.

For VBM analysis, the contrasts testing for the average effect (for example [1,0] in the first example; [1, 0, 0] or [0,1,0] in the second; and [1,0,0,0] or [0,1,0,0] in the third) are irrelevant.

In the following examples the letter "R" represents the regressor corresponding to the continuous covariate and r1, r2, r3, etc are the values of this regressor for subject 1, 2, 3, etc.